1. Of an animal, following the scent of something, typically another animal that is its prey. Once the fierce prediator is on the scent of its prey, it's unlikely it will stop pursuing it. They put the bloodhounds on the scent of the escaped prisoners.

2. By extension, having become attuned to the pursuit of something, especially due to having made some new observation or acquired some clue. You can always tell Detective Gomez is on the scent when he starts pinning things to the bulletin board. I've been to six different stores today, but I think I'm finally on the scent of it now after reading some reviews.